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A pair of bounded operators (S,P) which has the domain \\Gamme = {(z 1 +z 2, z 1z 2) : |z1|{\\leq} 1, |z2| {\\leq}1} {\\subseteq} C2 as a spectral set, is called a \\Gamme-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a \\Gamma-contraction (S,P). 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